|0 1J (a) Write A in terms of A and I. (b) Find A5 for the matrix Similarly, multiplying both sides of the equation A² = 2A + I by A gives A³ in terms of A², A, and I. Moreover, you can write A³ in terms of A and I by replacing A² with 2A + I, as shown below. A³ = 2A² + A = 2 (2A + I) + A = 5A+2I 4-1 го о A = 2 2 -1 1 0 2 (Hint: Find the characteristic polynomial of A, then use the Cayley-Hamilton Theorem to write A³ in terms of A², A, and I. Inductively write A5 in terms of A², A, and I.)

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